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Approximation in Morrey spaces
Publication . Almeida, Alexandre; Samko, Stefan
A new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalisation of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained. (C) 2016 Elsevier Inc. All rights reserved.
Embeddings of local generalized Morrey spaces between weighted Lebesgue spaces
Publication . Almeida, Alexandre; Samko, Stefan
We prove that local generalized Morrey spaces are closely embedded between weighted Lebesgue spaces. We show that such embeddings are strict in all the cases under consideration by constructing counterexamples. As a consequence, continuous embeddings between generalized Morrey spaces and generalized Stummel spaces are established, as well as between Stummel classes (vanishing Stummel spaces). In particular, we obtain embeddings into a new Stummel class of functions with some vanishing property at infinity. We also partially improve a known result on the coincidence of Stummel spaces with a modification of Morrey spaces where the supremum norm is replaced by an integral L-p-norm. (C) 2017 Elsevier Ltd. All rights reserved.
Homological lemmas for (Non-abelian) group-like structures by diagram chasing in a self-dual context
Publication . Dayaram, Kishan Kumar; Goswami, Amartya; Janelidze, Zurab; Rodelo, Diana; Linden, Tim Van der
Through abelian categories, homological lemmas for modules admit a self-dual treatment, where half of the proof of a lemma is sufficient to prove the full lemma. In this paper we show how the context of a ‘noetherian form’, recently introduced by the second and third authors, allows a self-dual treatment of these lemmas even in the case of non-abelian categories of group-like structures. This context covers a wide range of examples: module categories, the category of groups, of graded abelian groups, the categories of Lie algebras, of cocommutative Hopf algebras, the category of Heyting semilattices, of loops, the dual of the category of pointed sets, the category of modular/distributive lattices and modular connections, the category of sets and partial bijections, and many others. More generally, it includes all semi-abelian and Grandis exact categories.
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Fundação para a Ciência e a Tecnologia
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5876
Número da atribuição
UID/MAT/04106/2013